An exhaust purification system for an internal combustion engine is known in the art, in which a catalyst which forms a honeycomb structure is arranged in an engine exhaust passage, a fuel addition nozzle which secondarily feeds fuel or hydrocarbons is arranged in the exhaust passage upstream of the catalyst, and estimates a degree of clogging at an inflow end of the catalyst based on an amount of particulate matter which flows into the catalyst, an amount of fuel from the fuel addition nozzle, and a temperature of exhaust gas which flows into the catalyst (for example, see PTL 1). In PTL 1, when the degree of clogging reaches a predetermined upper limit degree, clogging removal processing is performed to remove the clogging at the inflow end of the catalyst.